If \(a_n=81\cdot\left(\frac{1}{3}\right)^{n-1}\), what is the value of \(a_4\)?
Answer and explanation
Correct answer: \(3\)
This is the explicit form of a geometric progression, \(a_n=a_1r^{n-1}\), where the first term is \(81\) and the common ratio is \(\frac13\). To find the fourth term, substitute \(n=4\), so the exponent is \(4-1=3\), not 4. Therefore, \(a_4=81\left(\frac13\right)^3=81\cdot\frac1{27}=3\). Hence option B is correct. Option A would result from using one extra power of \(\frac13\), while options C and D do not follow the required three successive multiplications by \(\frac13\).
Frequently asked questions
What is the correct answer to this question?
\(3\)
Why is this the correct answer?
This is the explicit form of a geometric progression, \(a_n=a_1r^{n-1}\), where the first term is \(81\) and the common ratio is \(\frac13\). To find the fourth term, substitute \(n=4\), so the exponent is \(4-1=3\), not 4. Therefore, \(a_4=81\left(\frac13\right)^3=81\cdot\frac1{27}=3\). Hence option B is correct. Option A would result from using one extra power of \(\frac13\), while options C and D do not follow the required three successive multiplications by \(\frac13\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
